Subgroups — C₁₃×#34259 #15720598

Order 3328.

5106 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2339	C₂	1	12	yes	maximal, complemented
6	C₁₃×#2311	C₂	1	3	yes	maximal, complemented
7	C₁₃×#2310	C₂	1	3	yes	maximal, complemented
8	C₁₃×#2297	C₂	1	3	yes	maximal, complemented
9	C₂×C₁₃×#391	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×2₋¹⁺⁴	—	2	8	no	—
11	C₂×C₁₃×2₋¹⁺⁴	—	2	8	no	—
12	C₂×C₁₃×2₋¹⁺⁴	C₄	1	16	yes	complemented
13	C₂²×C₁₃×#41	C₂²	1	3	yes	—
14	C₂²×C₁₃×#41	C₂²	1	6	yes	—
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₁₃	C₂²	1	3	yes	—
17	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#520	—	2	8	no	—
19	C₄×C₁₃×#41	—	2	8	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
24	C₂×C₁₃×#117	C₂²	1	3	yes	—
25	C₂×C₁₃×#117	C₂²	1	3	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
28	C₁₃×#391	C₂²	1	3	yes	—
29	C₁₃×#391	C₂²	1	6	yes	—
30	C₁₃×#391	C₂²	1	12	yes	—
31	C₁₃×#391	C₂²	1	3	yes	—
32	C₁₃×#391	C₂²	1	12	yes	—
33	C₁₃×#390	C₂²	1	1	yes	characteristic
34	C₁₃×#390	C₂²	1	3	yes	—
35	C₁₃×#386	C₂²	1	12	yes	—
36	C₁₃×#386	C₂²	1	12	yes	—
37	C₁₃×#381	C₂²	1	12	yes	—
38	C₁₃×#380	C₂²	1	12	yes	—
39	C₄×C₁₃×C₂²⋊C₄	C₂²	1	12	yes	—
40	C₂×C₁₃×#95	C₂²	1	12	yes	—
41	C₁₃×2₋¹⁺⁴	—	2	128	no	—
42	C₂×C₁₃×#41	—	2	24	no	—
43	C₂×C₁₃×#41	—	2	24	no	—
44	C₂×C₁₃×#41	—	2	12	no	—
45	C₂×C₁₃×#41	—	2	12	no	—
46	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
47	C₂×C₁₃×#41	C₂×C₄	1	48	yes	complemented
48	C₂×C₁₃×#41	C₂×C₄	1	24	yes	complemented
49	C₂×C₁₃×#41	D₄	1	8	yes	—
50	C₂×C₁₃×#41	D₄	1	8	yes	—
51	C₂²×Q₈×C₁₃	—	2	8	no	—
52	C₂²×Q₈×C₁₃	—	2	8	no	—
53	C₂²×Q₈×C₁₃	—	2	12	no	—
54	C₂²×Q₈×C₁₃	—	2	12	no	—
55	C₂²×Q₈×C₁₃	C₂×C₄	1	16	yes	complemented
56	C₂²×Q₈×C₁₃	C₂×C₄	1	24	yes	complemented
57	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
58	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
68	C₄×Q₈×C₁₃	—	2	8	no	—
69	C₄×Q₈×C₁₃	—	2	8	no	—
70	C₄×D₄×C₁₃	—	2	24	no	—
71	C₄×D₄×C₁₃	—	2	24	no	—
72	C₁₃×#117	—	2	12	no	—
73	C₁₃×#117	—	2	12	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	12	no	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
83	C₂×C₄²×C₁₃	—	2	12	no	—
84	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
85	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
88	C₁₃×#95	C₂³	1	12	yes	—
89	C₁₃×#95	C₂³	1	12	yes	—
90	C₁₃×#95	C₂³	1	24	yes	—
91	#34259	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
93	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
94	C₁₃×#41	—	2	192	no	—
95	C₁₃×#41	—	2	96	no	—
96	C₁₃×#41	C₂²⋊C₄	1	64	yes	complemented
97	C₂×Q₈×C₁₃	—	2	64	no	—
98	C₂×Q₈×C₁₃	—	2	96	no	—
99	C₂×Q₈×C₁₃	—	2	6	no	—
100	C₂×Q₈×C₁₃	—	2	12	no	—
101	C₂×Q₈×C₁₃	—	2	12	no	—
102	C₂×Q₈×C₁₃	—	2	6	no	—
103	C₂×Q₈×C₁₃	C₂²×C₄	1	24	yes	—
104	C₂×Q₈×C₁₃	C₂²×C₄	1	12	yes	—
105	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
106	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
107	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
108	C₂×D₄×C₁₃	—	2	12	no	—
109	C₂×D₄×C₁₃	—	2	12	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	C₂²×C₄	1	24	yes	—
113	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
114	C₂×D₄×C₁₃	C₂²×C₄	1	12	yes	—
115	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	—
116	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	—
117	C₂²×C₄×C₁₃	—	2	12	no	—
118	C₂²×C₄×C₁₃	—	2	12	no	—
119	C₂²×C₄×C₁₃	—	2	12	no	—
120	C₂²×C₄×C₁₃	—	2	12	no	—
121	C₂²×C₄×C₁₃	—	2	12	no	—
122	C₂²×C₄×C₁₃	—	2	12	no	—
123	C₂²×C₄×C₁₃	—	2	12	no	—
124	C₂²×C₄×C₁₃	—	4	6	no	—
125	C₂²×C₄×C₁₃	—	4	12	no	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	24	yes	—
127	C₂²×C₄×C₁₃	C₂²×C₄	1	24	yes	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
138	C₁₃×C₄⋊C₄	—	2	6	no	—
139	C₁₃×C₄⋊C₄	—	2	12	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	12	no	—
142	C₁₃×C₂²⋊C₄	—	2	12	no	—
143	C₁₃×C₂²⋊C₄	—	2	12	no	—
144	C₁₃×C₂²⋊C₄	—	2	8	no	—
145	C₁₃×C₂²⋊C₄	—	4	12	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	6	no	—
148	C₄²×C₁₃	—	2	12	no	—
149	C₄²×C₁₃	—	2	12	no	—
150	C₂²×2₋¹⁺⁴	C₂×C₁₃	1	1	yes	characteristic
151	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
153	Q₈×C₂²⋊C₄	C₂×C₁₃	1	4	yes	complemented
154	#2339	C₂×C₁₃	1	12	yes	complemented
155	#2311	C₂×C₁₃	1	3	yes	complemented
156	#2310	C₂×C₁₃	1	3	yes	complemented
157	#2297	C₂×C₁₃	1	3	yes	complemented
158	C₂×#391	C₂×C₁₃	1	3	yes	complemented
159	C₂³×C₁₃	—	2	6	no	—
160	C₂³×C₁₃	—	2	6	no	—
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
166	C₂³×C₁₃	C₂³×C₄	1	6	yes	—
167	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
168	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
169	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
170	Q₈×C₁₃	—	2	48	no	—
171	Q₈×C₁₃	—	2	24	no	—
172	Q₈×C₁₃	C₂×C₂²⋊C₄	1	16	yes	—
173	D₄×C₁₃	—	2	48	no	—
174	D₄×C₁₃	—	2	8	no	—
175	D₄×C₁₃	C₂×C₂²⋊C₄	1	48	yes	—
176	C₂×C₄×C₁₃	—	2	48	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	6	no	—
179	C₂×C₄×C₁₃	—	2	6	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	48	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	6	no	—
184	C₂×C₄×C₁₃	—	2	6	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	6	no	—
187	C₂×C₄×C₁₃	—	2	6	no	—
188	C₂×C₄×C₁₃	—	2	12	no	—
189	C₂×C₄×C₁₃	—	4	24	no	—
190	C₂×C₄×C₁₃	—	8	12	no	—
191	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	48	yes	—
192	C₂×C₄×C₁₃	C₂³×C₄	1	12	yes	—
193	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
194	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
195	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	complemented
200	C₂×2₋¹⁺⁴	—	2	8	no	—
201	C₂×2₋¹⁺⁴	—	2	8	no	—
202	C₂×2₋¹⁺⁴	C₄×C₁₃	1	16	yes	complemented
203	C₂²×#41	C₂²×C₁₃	1	3	yes	—
204	C₂²×#41	C₂²×C₁₃	1	6	yes	—
205	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
206	C₂³×Q₈	C₂²×C₁₃	1	3	yes	—
207	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
208	#520	—	2	8	no	—
209	C₄×#41	—	2	8	no	—
210	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
212	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
213	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
214	C₂×#117	C₂²×C₁₃	1	3	yes	—
215	C₂×#117	C₂²×C₁₃	1	3	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
217	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
218	#391	C₂²×C₁₃	1	3	yes	—
219	#391	C₂²×C₁₃	1	6	yes	—
220	#391	C₂²×C₁₃	1	12	yes	—
221	#391	C₂²×C₁₃	1	12	yes	—
222	#391	C₂²×C₁₃	1	3	yes	—
223	#390	C₂²×C₁₃	1	3	yes	—
224	#390	C₂²×C₁₃	1	1	yes	characteristic
225	#386	C₂²×C₁₃	1	12	yes	—
226	#386	C₂²×C₁₃	1	12	yes	—
227	#381	C₂²×C₁₃	1	12	yes	—
228	#380	C₂²×C₁₃	1	12	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₁₃	1	12	yes	—
230	C₂×#95	C₂²×C₁₃	1	12	yes	—
231	C₂²×C₁₃	—	2	12	no	—
232	C₂²×C₁₃	—	2	12	no	—
233	C₂²×C₁₃	—	2	6	no	—
234	C₂²×C₁₃	—	2	6	no	—
235	C₂²×C₁₃	—	2	4	no	—
236	C₂²×C₁₃	—	2	8	no	—
237	C₂²×C₁₃	—	4	4	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	12	yes	—
241	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
242	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
243	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
245	C₂²×C₁₃	#585	1	2	yes	—
246	C₄×C₁₃	—	2	12	no	—
247	C₄×C₁₃	—	2	4	no	—
248	C₄×C₁₃	—	4	6	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	4	6	no	—
251	C₄×C₁₃	C₂²×C₂²⋊C₄	1	12	yes	—
252	C₄×C₁₃	C₂²×C₂²⋊C₄	1	4	yes	—
253	2₋¹⁺⁴	—	2	128	no	—
254	C₂×#41	—	2	24	no	—
255	C₂×#41	—	2	24	no	—
256	C₂×#41	—	2	12	no	—
257	C₂×#41	—	2	12	no	—
258	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
259	C₂×#41	C₂×C₄×C₁₃	1	48	yes	complemented
260	C₂×#41	C₂×C₄×C₁₃	1	24	yes	complemented
261	C₂×#41	D₄×C₁₃	1	8	yes	—
262	C₂×#41	D₄×C₁₃	1	8	yes	—
263	C₂²×Q₈	—	2	8	no	—
264	C₂²×Q₈	—	2	8	no	—
265	C₂²×Q₈	—	2	12	no	—
266	C₂²×Q₈	—	2	12	no	—
267	C₂²×Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
268	C₂²×Q₈	C₂×C₄×C₁₃	1	24	yes	complemented
269	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
270	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
271	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
273	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
275	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
276	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
277	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
278	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
279	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
280	C₄×Q₈	—	2	8	no	—
281	C₄×Q₈	—	2	8	no	—
282	C₄×D₄	—	2	24	no	—
283	C₄×D₄	—	2	24	no	—
284	#117	—	2	12	no	—
285	#117	—	2	12	no	—
286	C₂×C₄⋊C₄	—	2	12	no	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
295	C₂×C₄²	—	2	12	no	—
296	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
297	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
298	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
299	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
300	#95	C₂³×C₁₃	1	12	yes	—
301	#95	C₂³×C₁₃	1	24	yes	—
302	#95	C₂³×C₁₃	1	12	yes	—
303	C₂×C₁₃	—	2	12	no	—
304	C₂×C₁₃	—	4	4	no	—
305	C₂×C₁₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₁₃	C₄×2₋¹⁺⁴	1	2	yes	—
307	C₂×C₁₃	#3489	1	2	yes	—
308	C₂×C₁₃	#3499	1	1	yes	characteristic
309	C₂×C₁₃	#3500	1	1	yes	characteristic
310	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
311	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
312	#41	—	2	192	no	—
313	#41	—	2	96	no	—
314	#41	C₁₃×C₂²⋊C₄	1	64	yes	complemented
315	C₂×Q₈	—	2	64	no	—
316	C₂×Q₈	—	2	96	no	—
317	C₂×Q₈	—	2	6	no	—
318	C₂×Q₈	—	2	12	no	—
319	C₂×Q₈	—	2	12	no	—
320	C₂×Q₈	—	2	6	no	—
321	C₂×Q₈	C₂²×C₄×C₁₃	1	24	yes	—
322	C₂×Q₈	C₂²×C₄×C₁₃	1	12	yes	—
323	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
324	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
325	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
326	C₂×D₄	—	2	12	no	—
327	C₂×D₄	—	2	12	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	C₂²×C₄×C₁₃	1	24	yes	—
331	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
332	C₂×D₄	C₂²×C₄×C₁₃	1	12	yes	—
333	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	—
334	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	—
335	C₂²×C₄	—	2	12	no	—
336	C₂²×C₄	—	2	12	no	—
337	C₂²×C₄	—	2	12	no	—
338	C₂²×C₄	—	2	12	no	—
339	C₂²×C₄	—	2	12	no	—
340	C₂²×C₄	—	2	12	no	—
341	C₂²×C₄	—	2	12	no	—
342	C₂²×C₄	—	4	6	no	—
343	C₂²×C₄	—	4	12	no	—
344	C₂²×C₄	C₂²×C₄×C₁₃	1	24	yes	—
345	C₂²×C₄	C₂²×C₄×C₁₃	1	24	yes	—
346	C₂²×C₄	C₂²×C₄×C₁₃	1	12	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
351	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
352	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
353	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
356	C₄⋊C₄	—	2	6	no	—
357	C₄⋊C₄	—	2	12	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	12	no	—
360	C₂²⋊C₄	—	2	12	no	—
361	C₂²⋊C₄	—	2	12	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	4	12	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	6	no	—
366	C₄²	—	2	12	no	—
367	C₄²	—	2	12	no	—
368	C₁₃	#34259	1	1	yes	characteristic, direct product factor, Sylow
369	C₂³	—	2	6	no	—
370	C₂³	—	2	6	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	2	4	no	—
375	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
376	C₂³	C₂³×C₄×C₁₃	1	6	yes	—
377	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
378	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
379	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
380	Q₈	—	2	48	no	—
381	Q₈	—	2	24	no	—
382	Q₈	C₂×C₁₃×C₂²⋊C₄	1	16	yes	—
383	D₄	—	2	48	no	—
384	D₄	—	2	8	no	—
385	D₄	C₂×C₁₃×C₂²⋊C₄	1	48	yes	—
386	C₂×C₄	—	2	48	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	6	no	—
389	C₂×C₄	—	2	6	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	48	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	6	no	—
394	C₂×C₄	—	2	6	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	6	no	—
397	C₂×C₄	—	2	6	no	—
398	C₂×C₄	—	2	12	no	—
399	C₂×C₄	—	4	24	no	—
400	C₂×C₄	—	8	12	no	—
401	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	48	yes	—
402	C₂×C₄	C₂³×C₄×C₁₃	1	12	yes	—
403	C₂×C₄	C₂³×C₄×C₁₃	1	6	yes	—
404	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
405	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
406	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
409	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	complemented
410	C₂²	—	2	12	no	—
411	C₂²	—	2	12	no	—
412	C₂²	—	2	6	no	—
413	C₂²	—	2	6	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	8	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	12	yes	—
420	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
421	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
422	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
423	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
424	C₂²	C₁₃×#585	1	2	yes	—
425	C₄	—	2	12	no	—
426	C₄	—	2	4	no	—
427	C₄	—	4	6	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	6	no	—
430	C₄	C₂²×C₁₃×C₂²⋊C₄	1	12	yes	—
431	C₄	C₂²×C₁₃×C₂²⋊C₄	1	4	yes	—
432	C₂	—	2	12	no	—
433	C₂	—	4	4	no	—
434	C₂	C₂³×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
435	C₂	C₄×C₁₃×2₋¹⁺⁴	1	2	yes	—
436	C₂	C₁₃×#3489	1	2	yes	—
437	C₂	C₁₃×#3499	1	1	yes	characteristic
438	C₂	C₁₃×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×2₋¹⁺⁴	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₃×#520	C₂	semidirect
3. C₂×C₄×C₁₃×#41	C₂	semidirect
4. Q₈×C₁₃×C₂²⋊C₄	C₂	semidirect
5. C₁₃×#2339	C₂	semidirect
6. C₁₃×#2311	C₂	semidirect
7. C₁₃×#2310	C₂	semidirect
8. C₁₃×#2297	C₂	semidirect
9. C₂×C₁₃×#391	C₂	semidirect
12. C₂×C₁₃×2₋¹⁺⁴	C₄	semidirect
47. C₂×C₁₃×#41	C₂×C₄	semidirect
48. C₂×C₁₃×#41	C₂×C₄	semidirect
55. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
56. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
91. #34259	C₁₃	direct (N × H)
96. C₁₃×#41	C₂²⋊C₄	semidirect
151. C₂×#520	C₂×C₁₃	semidirect
152. C₂×C₄×#41	C₂×C₁₃	semidirect
153. Q₈×C₂²⋊C₄	C₂×C₁₃	semidirect
154. #2339	C₂×C₁₃	semidirect
155. #2311	C₂×C₁₃	semidirect
156. #2310	C₂×C₁₃	semidirect
157. #2297	C₂×C₁₃	semidirect
158. C₂×#391	C₂×C₁₃	semidirect
199. C₂×C₄×C₁₃	2₋¹⁺⁴	semidirect
202. C₂×2₋¹⁺⁴	C₄×C₁₃	semidirect
259. C₂×#41	C₂×C₄×C₁₃	semidirect
260. C₂×#41	C₂×C₄×C₁₃	semidirect
267. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
268. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
314. #41	C₁₃×C₂²⋊C₄	semidirect
368. C₁₃	#34259	direct (N × H)
409. C₂×C₄	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×2₋¹⁺⁴	2
C₂×C₁₃×#520	2
C₂×C₄×C₁₃×#41	2
Q₈×C₁₃×C₂²⋊C₄	2
C₁₃×#2339	2
C₁₃×#2311	2
C₁₃×#2310	2
C₁₃×#2297	2
C₂×C₁₃×#391	2
#34259	13

Subgroups — C13×#34259 #15720598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34259 #15720598